Climate Change: Day 10
date: September 25, 2014
Last Time: jet stream, arctic amplification, extra-tropical cyclones, more hot days in Tally
L = "http://myweb.fsu.edu/jelsner/PW_US.txt"
df = read.table(L, header = TRUE)
head(df)## Month Year AvgPW MoA PW
## 1 1 1958 0.2968 Jan 0.7538
## 2 1 1959 0.3324 Jan 0.8443
## 3 1 1960 0.3399 Jan 0.8634
## 4 1 1961 0.2716 Jan 0.6900
## 5 1 1962 0.3124 Jan 0.7934
## 6 1 1963 0.2688 Jan 0.6828library(ggplot2)
ggplot(df, aes(x = Year, y = PW)) +
geom_line() +
geom_smooth(method = lm) +
facet_wrap(~ Month, nrow = 1) +
ylab("US Avg Monthly Precipitable Water (cm)") +
theme_bw()
Slower moving jet stream together with more moisture (water vapor) increases the chance for heavy rainfall.
The atmosphere’s ability to hold water (recall: saturation vapor pressure vs temp) increases by about 4 percent for every 1°F increase in temperature
1-in-100 year event. Return periods versus annual probability.
Today: tropical cyclones, heat engine, MPI vs LI
\[ \hbox{MPI} \sim \frac{\hbox{SST}}{T_o}\hbox{BL}_{f}(\hbox{SST}) \]
MPI (maximum potential intensity) is the highest wind speed (rotational) in units of meters per second.
SST is the ocean temperature at the surface, \(T_o\) is the temperature at the top of the hurricane and BL\(_{f}\)(SST) is the heat flux near the ocean surface. The heat flux depends on SST.
Extreme value theory (EVT) is a statistical theory that estimates the risk of extreme, rare events.
Suppose we record the highest wind speed (m s\(^{-1}\)) from 10 consecutive hurricanes.
- 34.5, 44.2, 57.5, 33.8, 67.8, 38.2, 41.5, 71.2, 61.0, 49.1
We order the values from lowest to highest.
- 33.8, 34.5, 38.2, 41.5, 44.2, 49.1, 57.5, 61.0, 67.8, 71.2
This tells us that 20% of the hurricanes have winds that exceed 61 m s\(^{-1}\) and 10% have winds that exceed 67.8 m s\(^{-1}\). EVT uses these quantile wind speeds to work out a theoretical highest possible wind speed, which we will call the limiting intensity (LI).
